13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- can be used to reflect the effects of the notch root stress concentration instead of Kt. It is remarkable that the ϕ(a) tends to the notch root stress concentration factor as the crack length a tends to zero. ( ) ( ) 0 K a a a α ϕ σ π Δ = ⋅ ⋅Δ ⋅ + (8) According to these theories, Meggiolaro et al. have proposed an effective method which could analytically estimate the Kf (see [9]). They associated ΔK and ΔKth(a) so that the short crack will propagate when: ( ) ( ) ( ) 2 1 th 0 0 K a a K a K 1 a a − ⎡ ⎤ Δ = ⋅ ⋅Δ >Δ =Δ ⋅ + ⎢ ⎥ ⎣ ⎦ γ γ η ϕ ρ σ π (9) Accordingly, a crack propagation criterion was stated using two dimensionless functions ϕ and g with the following expression: ( ) ( ) ( ) ( ) 0 0 0 0 0 1 0 0 0 K S S S K a g a , , , S a K S γ γ γ ρ σ ϕ γ ρ ρ σ ρ η π ρ ρ Δ Δ ⋅ Δ Δ ⎛ ⎞ Δ Δ ⎛ ⎞ > ≡ ⎜ ⎟ ⎜ ⎟ Δ ⎝ ⎠ Δ ⎝ ⎠ ⎡ ⎤ + Δ Δ ⎢ ⎥ ⎣ ⎦ (10) The second term ΔS0/Δ σ in the function g will be equal to the Kf when the Δ σ corresponds to the minimum stress range that can cause crack initiation and propagation from the notch border by fatigue, without arrest. In general, Kf and amax can always be found by solving the system ( ) 1 0 max max f max max f a a g ,K , , g g x a a x g ,K , , x ϕ κ γ ϕ ρ ρ ϕ ϕ κ γ ρ ρ ⎧ ⎛ ⎞ ⎛ ⎞ = ⎪ ⎜ ⎟ ⎜ ⎟ ⎧ = ⎪ ⎝ ⎠ ⎝ ⎠ ⇒ ⎨ ⎨ ∂ ∂ = ⎛ ⎞ ⎛ ⎞ ⎩ ⎪ ∂ ∂ =∂ ∂ ⎜ ⎟ ⎜ ⎟ ⎪ ⎝ ⎠ ⎝ ⎠ ⎩ (11) To verify the accuracy of the models to evaluate the tolerance to short cracks, a methodology is proposed to design notched fatigue test specimens specially conceived to induce non-propagating short cracks. The geometric configuration is that of a modified compact tension specimen C(T), having a machined notch with a circular hole with radio ρ at the tip, as is shown in 错误！未找到 引用源。a. The line of size a represents the crack length. The external dimensions and the notch length ( ) b mm 15 = is chosen according to ASTM E647 recommendations to assure that the loading condition at the crack tip is not influenced by the loading-pin holes. (a) (b) Fig. 4 a) Modified C(T) specimens, dimensions in mm.
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